Problem Detail: I’ve heard of (structural) induction. It allows you to build up finite structures from smaller ones and gives you proof principles for reasoning about such structures. The idea is clear enough. But what about coinduction? How does it work? Read More …
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Convolutional Neural Network Example in Tensorflow
Problem Detail: I want to ask the dimension change in different convolution and max-pooling layer. I am referring to the example in TensorFlow tutorial: http://tensorflow.org/tutorials/mnist/pros/index.html#deep-mnist-for-experts The original image is a 28x28x1 The first convolutional layer: apply convolution to a 5×5 patch Read More …
Constructing of Double Connected Edge List (DCEL)
Problem Detail: For a given planar graph $G(V,E)$ embedded in the plane, defined by list of segments $E= left { e_1,…,e_m right } $, each segment $e_i$ is represented by its endpoints $left { L_i,R_i right }$. Construct a DCEL Read More …
Counting inversions in a list of integers using divide and conquer techniques
Problem Detail: This is a homework. It looks easy, but not really. A list of integers $a_n$, for every $i<j$, if $a_i>2a_j$, then it is an inversion. Count the inversions in the list, and return the count and the ordered list. Read More …
Algorithm for building a suffix array in time $O(n log^2 n)$
Problem Detail: I’ve been working with suffix arrays lately, and I can’t find an efficient algorithm for building a suffix array which is easy to understand. I have seen in many sites that there is an $O(n log^2 n)$ algorithm, but Read More …
Halting problem reducing to the blank tape halting problem
Problem Detail: I was going through my book of proof and I find very confusing its definition, so I would like someone to help me in understanding this. The blank tape problem takes a machine and an empty tape and tells Read More …
Appropriate minor to go with CS major
Problem Detail: I thought this would be the best place for a question like this. Anyway, I was wondering what minor would go well with a Computer Science degree. I was considering a minor in math but I am not entirely Read More …
What is the complexity of this matrix transposition?
Problem Detail: I’m working on some exercises regarding graph theory and complexity. Now I’m asked to give an algorithm that computes a transposed graph of $G$, $G^T$ given the adjacency matrix of $G$. So basically I just have to give an Read More …
What exactly (and precisely) is “hash?”
Problem Detail: I have heard the word “hash” being used in different contexts (all within the world of computing) with different meanings. For example, in the book Learn Python the Hard Way, in the chapter on dictionaries it is said “Python Read More …
Time complexity of a compiler
Problem Detail: I am interested in the time complexity of a compiler. Clearly this is a very complicated question as there are many compilers, compiler options and variables to consider. Specifically, I am interested in LLVM but would be interested in Read More …
